If the points (x, y) is collinear with the points (a, 0) and (0, b) prove that
=1.

Let the points be A(x, y), B(a, 0) and C(0, b). As the points are collinear, area of triangle ABC is zero.
The condition for collinearity of three given points (x ₁ , y ₁ ), (x ₂ , y ₂ ) and (x ₃ , y ₃ ) is
x ₁ (y ₂ – y ₃ ) + x ₂ (y ₃ – y ₁ ) + x ₃ (y ₁ – y ₂ ) = 0.

⇒ x(0 – b) + a(b – y) + 0(y – 0) = 0.

⇒ -bx + ab – ay = 0
⇒ bx + ay = ab